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An inverse problem solution for undetermined electrostatic force microscopy setups using neural networks.

G M Sacha¹, F B Rodríguez, P Varona

¹Grupo de Neurocomputación Biológica, Departamento de Ingeniería Informática, Escuela Politécnica Superior, Universidad Autónoma de Madrid, Cantoblanco, Madrid E-28049, Spain.

|May 7, 2009

Summary

This study introduces a novel method combining electrostatic theory and artificial neural networks (ANNs) to solve inverse problems in scanning probe microscopy. The technique accurately estimates unknown parameters like dielectric constants, even with unknown tip shapes.

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Area of Science:

Physics
Materials Science
Computational Science

Background:

Scanning probe microscopy (SPM) relies on understanding tip-sample interactions.
Solving inverse problems in SPM is challenging due to underdetermined systems.
Accurate characterization of material properties requires precise parameter estimation.

Purpose of the Study:

To develop a robust method for solving inverse problems in SPM using artificial neural networks (ANNs).
To estimate unknown parameters, such as tip-sample distance and dielectric constants, in complex SPM setups.
To validate the proposed technique with experimental data for real-world applicability.

Main Methods:

A hybrid approach combining theoretical electrostatic interactions with ANNs.

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Utilizing the generalized image charge method to generate training data for ANNs.

Training and validating ANNs on electrostatic interaction curves.

Applying the method to systems with known and unknown tip geometries.

Main Results:

Simultaneous estimation of tip-sample distance and dielectric constant for a tip over a metallic nanowire.
Quantitative estimation of dielectric constants in highly undetermined systems with unknown tip shapes (three free parameters).
Successful validation of the ANN-based method against experimental SPM data.

Conclusions:

The combined theoretical and ANN approach effectively solves inverse problems in SPM.
This method enables accurate material property estimation in complex and underdetermined scenarios.
The technique offers a powerful tool for advancing SPM applications in materials characterization.